I've done this several times, as I do not like hand stitching the binding, at least not enough to do it often or on every quilt. I often use solid colored fleece for a backing, so using a cotton print for the facing on the back adds a nice touch. My only concern is that I've read that the seam on the edges doesn't hold up over the long haul when it's unprotected, which might be an issue with a baby blanket. I can see where that might be true, since the traditional binding covers and preserves that seam. On the other hand, this method is quick and easy. I found it works best if there's a border around the front, so that when you stitch down the facing on the back, the stitch line is just a quilt line on the front.
There is another way to deal with the corners that's different from the triangular cuffs in the video. I use these two tutorials to help me:
https://ukcitycrafter.wordpress.com/...sible-binding/
https://thesillyboodilly.blogspot.co...y-to-face.html